A384952 Decimal expansion of the volume of an elongated pentagonal orthobirotunda with unit edge.

2, 1, 5, 2, 9, 7, 3, 4, 7, 7, 9, 1, 8, 7, 5, 3, 7, 6, 4, 6, 2, 5, 1, 7, 1, 8, 5, 0, 1, 4, 9, 7, 5, 5, 7, 2, 2, 7, 0, 9, 8, 5, 0, 7, 3, 7, 7, 7, 4, 3, 8, 0, 3, 9, 5, 3, 0, 3, 2, 0, 9, 9, 4, 8, 7, 9, 3, 3, 6, 3, 4, 1, 7, 7, 2, 1, 1, 5, 0, 7, 8, 4, 4, 4, 7, 7, 3, 2, 5, 1

Offset

2,1

Comments

The elongated pentagonal orthobirotunda is Johnson solid J_42.

Also the volume of an elongated pentagonal gyrobirotunda (Johnson solid J_43) with unit edge.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Wikipedia, Elongated pentagonal gyrobirotunda.

Wikipedia, Elongated pentagonal orthobirotunda.

Formula

Equals (45 + 17*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (45 + 17*A002163 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 1296*x^4 - 38880*x^3 + 252360*x^2 - 329400*x - 332975.

Example

21.52973477918753764625171850149755722709850737774...

Mathematica

First[RealDigits[(45 + 17*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J42", "Volume"], 10, 100]]

Crossrefs

Cf. A179451 (surface area - 10), A344149 (surface area + 20).

Cf. A002163, A010476, A384283, A384285, A384624, A384871, A384909, A384910.

Sequence in context: A082010 A318972 A341495 * A337943 A389413 A275213

Adjacent sequences: A384949 A384950 A384951 * A384953 A384954 A384955

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 20 2025

Status

approved